What is (\partial)/(\partial x)(2(x+v(x,t)t)) ?

The answer to (\partial)/(\partial x)(2(x+v(x,t)t)) is 2(1+t(\partial)/(\partial x)({v}(x,t)))

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(\partial)/(\partial x)(2(x+v(x,t)t))

\frac{\partial}{\partial x} (2 (x + v (x, t) t))

2 (1 + t \frac{\partial}{\partial x} (v (x, t)))

Solution steps

\frac{\partial}{\partial x} (2 (x + v (x, t) t))

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{\partial}{\partial x} (x + v (x, t) t)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 (\frac{\partial}{\partial x} (x) + \frac{\partial}{\partial x} (v (x, t) t))

\frac{\partial}{\partial x} (x) = 1

\frac{\partial}{\partial x} (v (x, t) t) = t \frac{\partial}{\partial x} (v (x, t))

= 2 (1 + t \frac{\partial}{\partial x} (v (x, t)))

(t - 4) e^{3 t}

7 (x^{2} + 3 x)^{6} (2 x + 3)

y = \frac{3}{x ^{2}} - \frac{4}{x ^{3}}

\int e^{\frac{x}{60}} d x

\frac{d ^{2}}{d x ^{2}} (2 a x - x^{2})

What is (\partial)/(\partial x)(2(x+v(x,t)t)) ?
The answer to (\partial)/(\partial x)(2(x+v(x,t)t)) is 2(1+t(\partial)/(\partial x)({v}(x,t)))